Scattering of acoustic phonons by rare earth substitutional atoms in yttrium aluminum garnets

The diffusive maxima of phonon signals, and in particular their arrival timest _m are examined for a number of solid solutions of rare earth atoms in yttrium aluminum garnets. The phonon pulses are generated by metallic films of the characteristic lengthl _h heated by current pulses to the temperatureT _h slightly higher than the ambient temperatureT. The injected phonons travel in wafers of the thicknessL _z. They are scattered by substitutional atoms of rare earth occupying the yttrium dodecahedral sites, rare earth and yttrium atoms occupying the aluminum octahedral sites and by another lattice imperfections generated in the process of sample growing. The qualitative analysis based on our exact formula for the diffusion coefficientD allows us to extract the contribution of rare earth atoms substituting the Y atoms toD. Considering the dependence oft _m/L _z ² on the temperature and the ratiol _h/L_z we conclude thatD～T _h ^?4 and that the energy of phonons forming the diffusive maxima ranges from 3.2k _BT_H to 4.2k _BT_H, which is in reasonable agreement with the existing estimates.     

Phonon focussing patterns: Calculation of response of finite area detectors to pulsed ballistic beams of dispersive and dispersionless phonons

The phonon images of crystals are described in the frame of the Boltzmann kinetic equation. Monochromatic heat pulses of the dispersive and dispersionless acoustic phonons are considered. Exact expressions for the energy and quasimomentum carried by a pulsed beam of monochromatic dispersionless acoustic phonons falling onto a detector of the finite area are derived. These formulae provide us with a convenient starting point for numerical calculations of phonon images. For the example of long wave-length acoustic phonons and a point as well as extended sources, an algorithm for numerical calculations of phonon images of anisotropic crystalline media is presented. However, it is quite general and can be easily adapted for dispersive phonons and to quasiparticles with an arbitrary dispersion low.     

Magnetic properties of some rare earth tellurate garnets

The magnetic properties of the lanthanide tellurate garnets Ln₃Te₂Li₃O₁₂ for Ln=Pr, Nd, Gd-Er, and Yb are found to exhibit similarities in many cases to the related aluminum or gallium garnet compounds. Magnetic exchange is also roughly comparable in magnitude, despite the systematic difference in exchange pathways.     

Coherent X-ray scattering by phonons

Interference effects arising from coherently coupled X-ray beams inelastically scattered from phonons have been used to determine phonon eigenvectors in Si and GaAs crystals. An outline of the method, experimental requirements, and theoretical background is presented. The experimental results are analyzed with the help of different lattice dynamical model calculations. Best overall agreement is found with phonon eigendata based on the bond charge model.     

Dispersive phonon imaging of InAs

The phonon-focusing patterns of ballistic phonons in InAs are measured in the frequency range 0.1 to 1 THz, in an effort to test the global validity of lattice dynamics models for this semiconductor. Phonon caustic patterns depend sensitively on the shapes of constant frequency surfaces. Several tunnel-junction detectors with sensitivity onsets in this frequency range are used to measure dispersive shifts in the phonon caustics. The measured caustic positions are compared to those predicted by rigid-ion and bond-charge models. Similar to the case of InSb studied by Hebboul and Wolfe, a 6-parameter bond-charge model (BCM)-with force constants determined by neutron, X-ray, and Raman scattering-reproduces the phonon-imaging data both qualitatively and quantitatively. Comparisons of the focusing patterns with an 11-parameter rigid-ion model (RIM) do not show good agreement. New structures are predicted in the phononfocusing patterns at frequencies above about 1.2 THz — presently outside our experimental range-which are highly sensitive to the theoretical modeling.     

Scattering of long-wavelength acoustic phonons by isotopic impurities

We consider the problem of the relaxation of an arbitrary initial distribution function of a gas of long-wave acoustic phonons scattered by isotopic impurities embedded in a crystalline medium with cubic symmetry. The spectral decomposition of the collision integral of the suitable Boltzmann-Peierls equation is obtained. The spectrum of the collision operator is purely discrete and in addition to the eigenvalue 0 consists of three other eigenvalues. Explicit analytic expressions for these eigenvalues are obtained. Within the Chapman-Enskog approximation we derive the diffusion equation for the density of phonons and obtain the explicit expression for the diffusion coefficient. The dependency of the eigenvalues of the collision operator and the diffusion coefficient on the elastic constants of the medium is studied.     

Picosecond X-ray diffraction studies of laser-excited acoustic phonons in InSb

We have employed time-resolved X-ray diffraction with picosecond temporal resolution to measure the time-dependent rocking curves of laser-irradiated asymmetrically cut single InSb crystals. Coherent acoustic phonons were excited in the crystals by irradiation with 800-nm, 100-fs laser pulses at irradiances between 0.25 and 12 mJ/cm². The induced time-dependent strain profiles (corresponding to the coherent phonons) were monitored by diffracting collimated, monochromatic pulses of X-rays from the irradiated crystals. Recording of the diffracted radiation with a fast low-jitter X-ray streak camera resulted in an overall temporal resolution of better than 2 ps. The strain associated with the coherent phonons modifies the rocking curve of the crystal in a time-dependent manner, and the rocking curve is recorded by keeping the angle of incidence of the X-rays upon the crystal fixed, but varying the energy of the incident X-rays around a central energy of 8.453 keV (corresponding to the peak of the rocking curve of the unperturbed crystal). The observed time-dependent diffraction from the irradiated crystals is in reasonable agreement with simulations over a wide range of energies from the unperturbed rocking-curve peak. Received: 22 March 2002 / Revised version: 25 March 2002 / Published online: 6 June 2002     

Room temperature magnetization measurements of some substituted rare earth iron garnets

The saturation magnetization (M _s) and the initial magnetic susceptibility (χ _in) of substituted yttrium iron garnet (YIG) Ho_3−x Y _x Fe₅O₁₂ where (x=0,0.3,1.5), pure terbium iron garnet Tb₃Fe₅O₁₂, and substituted aluminum iron garnet (AlIG) Ho₃Fe_5−x Al _x O₁₂ where (x=0.05,0.7) at room temperature are reported. It has been observed that M _s and χ _in decrease in a linear manner as Ho³⁺ replaces Y³⁺ in yttrium iron garnet. For substituted (AlIG), a drastic decrease in both M _s and χ _in as Al³⁺ ions replace Fe³⁺ ions. The rate of decrease of M _s and χ _in with the increase of Al³⁺ for substituted (AlIG) is greater than that for substituted (YIG). That is attributed to the decrease in the superexchange interaction (self and mutual iron interactions) with Al substitution.     

On the path length of an excess electron interacted with optical phonons in a molecular chain

We show that in a molecular chain with dispersionless phonons at zero temperature, a “quasistationary” moving soliton state of an excess electron is possible. As the soliton velocity vanishes, the path length of the excess electron exponentially tends to infinity. It is demonstrated that in the presence of dispersion, when the soliton initial velocity exceeds the maximum group velocity of the chain, the soliton slows down until it reaches the maximum group velocity and then moves stationarily at this maximum group velocity. A conclusion is made of the fallacy of some works were the existence of moving polarons in a dispersionless medium is considered infeasible.     

Effect of Nonlinearity on Scattering Dynamics of Solitary Waves

We discuss the effect of nonlinearity on the scattering dynamics of solitary waves. The pure nth power model with the interaction potential V （Х） = Х^n/n is present, which is a paradigm model in the study of solitary waves. The dependence of the scattering property on nonlinearity is closely related to the topological structures of the solitary waves. Moreover, for one of the four collision types, the rates of energy loss increase with the strength of nonlinearity and would reach 1 at n ≥ 10, which means that the two solitary waves would become of fragments completely after the collision.     

Anomalous Heat Conduction in One-Dimensional Dimerized Lattices

The process of heat conduction in one-dimensional dimerized systems is studied by means of numerical simulation. Taking into account the difference between the strong bond and the weak one of the systems, our calculation indicates that heat conduction in the lattice is anomalous. For the typical parameter related to a real physical system, the divergent exponent is shown to be in agreement with that predicted by the mode-coupling theory. Moreover, our study shows that the homogeneous chain is the best thermal conductor.     

Scattering of thermal phonon pulses by isotopes in silicon

The pure ballistic propagation of acoustic phonons in crystals at low temperatures can be described within anisotropic continuum acoustics. One needs only the elastic constants and mass densities to calculate the time-dependent spectral phonon irradition of the bolometer for a given radiator pulse power and detector/radiator geometry. We extend this treatment by including single isotope-scattering events for the phonons in a (111)-cut silicon disk on their flight from the radiator to the detector. Using the earlier experimentally determined polarization and frequency dependent phonon absorption in the bolometer metal, the instantaneous temperature of the bolometer can be calculated from this irradiation. This allows a direct comparison with measured bolometer temperatures using exactly the same transmission or reflection arrangement as in calculation. A very satisfying agreement is observed in the expected range of single phonon scattering.     

Renormalization of transversal phonons in mixed valent rare earth compounds

The possibility of a softening of transversal acoustic phonons in mixed valent rare earth compounds is demonstrated. The effect should be largest at the zone boundary.     

The effects of LO phonons on charge qubit

In this paper, we study the influence of LO phonon (LOP) on the charge qubit in a quantum dot (QD), and find that the eigenenergies of the ground and first excited states are reduced due to the electron-LOP interaction. At the same time, the time evolution of the electron probability density is obtained, the dependence of the oscillating period on electron-LOP coupling constant is found, the relation of between the oscillating period and the confinement length of the QD is calculated. Finally, we consider the effects of the electron-LOP coupling constant on pure dephasing factor under considering the correction of electron-LOP interaction for the wave functions. Our results suggest that electron-LOP interaction has very important effects on charge qubit.     

Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling

A two-dimensional nonlinear Schrödinger lattice with nonlinear coupling, modelling a square array of weakly coupled linear optical waveguides embedded in a nonlinear Kerr material, is studied. We find that despite a vanishing energy difference (Peierls-Nabarro barrier) of fundamental stationary modes the mobility of localized excitations is very poor. This is attributed to a large separation in parameter space of the bifurcation points of the involved stationary modes. At these points the stability of the fundamental modes is changed and an asymmetric intermediate solution appears that connects the points. The control of the power flow across the array when excited with plane waves is also addressed and shown to exhibit great flexibility that may lead to applications for power-coupling devices. In certain parameter regimes, the direction of a stable propagating plane-wave current is shown to be continuously tunable by amplitude variation (with fixed phase gradient). More exotic effects of the nonlinear coupling terms like compact discrete breathers and vortices, and stationary complex modes with nontrivial phase relations are also briefly discussed. Regimes of dynamical linear stability are found for all these types of solutions.     

Theoretical study of NMR relaxation due to rattling phonons

We calculate the NMR relaxation rate due to quadrupolar coupling of the nucleus to a local, strongly anharmonic phonon mode. As a model potential for a “rattling” motion we consider a square-well potential. We calculate the free phonon Green's function analytically and derive the low and high temperature limits of the NMR relaxation rate. It is shown that the temperature dependence of the NMR relaxation rate possesses a peak in contrast to harmonic phonons but in qualitative agreement with a recent NMR study on KOs₂O₆. We discuss the influence of phonon renormalization due to electron-phonon interaction.     

Effect of changing incident wavelength on Raman features of optical phonons in SiC nanorods and TaC nanowires

Novel Raman scattering in polar semiconductor SiC and TaC one-dimensional materials have been carried out. With increasing incident laser wavelength from 488 to 633 nm there is a huge difference in Raman intensity enhancement for the LO/IF peaks and the TO peak. This has been interpreted as due to Fröhlich interaction and abundant defects in polar nano-scale semiconductor materials.     

Proton-exchange influence on the polar phonons of LiTaO3 optical waveguides

Refractive index change and Raman scattering of Z-cut proton-exchanged LiTaO₃ optical waveguides with different composition have been studied. Probing of the waveguide depth was carried out by using micro-Raman spectroscopy in order to distinguish layers with different phase states. Varying the proton-exchange and post-exchange annealing regimes, two phases –α and β– in addition to the pure LiTaO₃, were clearly observed. The behaviour of the A ₁ vibrations of the TaO₆ groups was found to be very sensitive to the phase changes. Using data from waveguide Raman spectra, normal and oblique E(TO, LO) phonons were sorted and their properties were followed in the α and β phases. The OH-stretchings are considered to correspond to dipoles turned out of the oxygen planes. Received: 9 July 1999 / Accepted: 11 October 1999 / Published online: 24 March 2000     

General behavior of longitudinal optical phonons in cubic diatomic crystals

A general relationship for longitudinal optical (LO) phonons in diatomic cubic crystals is introduced. The analysis of spectroscopic data of diatomic cubic crystals reveals that LO frequencies correlate directly with bulk moduli in a nearest-neighbor fashion. The proportionality constant is found to be dependent only on lattice geometries. Transverse effective charges can be obtained when the Lyddane-Sachs-Teller is incorporated into the model. Our calculations are in excellent agreement with experimental values and theoretical calculations. Some interesting implications of the model are discussed.